# Parameter estimation of ARIMA model with exogenous variables (ARIMAX)

I am trying to compare an ARIMA model based on the price of a cryptocurrency without exogenous variables to one which adds in the number of tweets about the crypto in the same period as an exogenous variable.

I'm using the traditional box-jenkins method of estimating the best model and parameters using autocorrelation and partial autocorrelation plots. Despite being outdated i settled on this instead of using AIC or similar metrics. ( i am a beginner )

How do i estimate the parameters for my model once i am introducing the exogenous variables? Is there a way to use these same correlation plots on these?

I am also performing a grid search on the endogenous variable alone as well as with the exogenous variable the result of which is that the same or very similar parameters perform best (using RMSE).

Any insight would be very helpful! thanks

• I would say if you are a beginner to use the AIC rather than the plots. This also solves the issue of your exogenous variables because you still just take the model which has the lowest AIC. May 12 at 14:37
• You probably mean to ask about lag orders (which are hyperparameters) rather than proper parameters (which are the intercept and the "slope coefficients"). May 12 at 15:15
• One thing that confuses me is whether you are using multivariate arima (this has various names such as ArimaX) or not. To show how an exogenous variables impacts something this is really what you should run (although to me it is too complex, so I study other methods). You have to pre-white the predictors and the dependent variables which is why it is not worth the effort in my opinion . May 13 at 17:32
• Yes i am using a multivariate ARIMA (ARIMAX). What do you mean with pre-whiting the predictors? May 15 at 14:20

If you want to do it the Box-Jenkins way, you can first run a simple regression of $$Y$$ (endogenous) on $$X$$ (exogenous), obtain the residuals and then treat them as the variable of interest of an ARMA model. I.e. you would inspect the residuals' ACF and PACF in the Box-Jenkins manner.